Statement I: In Young's experiment, for two coherent sources, the resultant intensity is given by `I = 4 I_(0) cos^(2) ((phi)/(2))`
Statement II: Ratio of maximum to minimum intensity is `(I_(max))/(I_(min)) = ((sqrt I_(1) + sqrt I_(2))^(2))/((sqrt I_(1) - sqrt I_(2))^(2))`.

Options

A. Statement I is True, statement II is True, Statement II is a correct explanation for Statement I.
B. Statement I is Ture, Statement II is Ture, Statement II is NOT a correct explanation for Statement I.
C. Statement I is True, Statement II is False.
D. Statement I is False, Statement II is True.

Explanation

To solve the problem, we need to analyze both statements regarding Young's double-slit experiment and determine their validity.

### Step 1: Analyze Statement I
**Statement I:** In Young's experiment, for two coherent sources, the resultant intensity is given by \( I = 4 I_0 \cos^2 \left( \frac{\phi}{2} \right) \).

1. **Understanding Resultant Intensity:**
- The resultant intensity \( I \) when two coherent sources interfere is given by the formula:
\[ I = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos(\phi) \]
- Here, \( I_1 \) and \( I_2 \) are the intensities of the two sources, and \( \phi \) is the phase difference between them.

2. **Assuming Equal Intensities:**
- If the two sources have equal intensities, we can set \( I_1 = I_2 = I_0 \).
- Substituting this into the formula gives:
\[ I = I_0 + I_0 + 2\sqrt{I_0 I_0} \cos(\phi) = 2I_0 + 2I_0 \cos(\phi) \]
- Factoring out \( 2I_0 \):
\[ I = 2I_0 (1 + \cos(\phi)) \]

3. **Using Trigonometric Identity:**
- We know that \( 1 + \cos(\phi) = 2 \cos^2\left(\frac{\phi}{2}\right) \).
- Therefore:
\[ I = 2I_0 \cdot 2 \cos^2\left(\frac{\phi}{2}\right) = 4 I_0 \cos^2\left(\frac{\phi}{2}\right) \]
- Thus, **Statement I is correct**.

### Step 2: Analyze Statement II
**Statement II:** Ratio of maximum to minimum intensity is given by:
\[ \frac{I_{\text{max}}}{I_{\text{min}}} = \frac{(\sqrt{I_1} + \sqrt{I_2})^2}{(\sqrt{I_1} - \sqrt{I_2})^2} \]

1. **Finding Maximum and Minimum Intensities:**
- The maximum intensity \( I_{\text{max}} \) occurs when \( \cos(\phi) = 1 \):
\[ I_{\text{max}} = I_1 + I_2 + 2\sqrt{I_1 I_2} = \sqrt{I_1} + \sqrt{I_2})^2 \]
- The minimum intensity \( I_{\text{min}} \) occurs when \( \cos(\phi) = -1 \):
\[ I_{\text{min}} = I_1 + I_2 - 2\sqrt{I_1 I_2} = (\sqrt{I_1} - \sqrt{I_2})^2 \]

2. **Calculating the Ratio:**
- Therefore, the ratio of maximum to minimum intensity is:
\[ \frac{I_{\text{max}}}{I_{\text{min}}} = \frac{(\sqrt{I_1} + \sqrt{I_2})^2}{(\sqrt{I_1} - \sqrt{I_2})^2} \]
- Thus, **Statement II is also correct**.

### Conclusion
Both statements are correct, but Statement II does not provide a direct explanation for Statement I. Therefore, the final answer is:

- **Statement I is true.**
- **Statement II is true.**
- **Statement II is not a correct explanation for Statement I.**